In a vessel containing \(SO_3\), \(SO_2\) and \(O_2\) at equilibrium some helium gas is introduced so that the total pressure increases while temperature and volume remains constant. According to Le Chatelier’s principle, the dissociation of \(SO_3\)

remains unaltered

The correct answer is option 3.  remains unaltered.

The given conditions are:

The volume of the vessel is constant.

Temperature is constant.

Helium gas is introduced, increasing the total pressure.

Analysis:

Constant Volume and Total Pressure Increase:

When helium gas is added to the vessel, the total pressure increases. However, since the volume is constant, the partial pressures of \(SO_3\), \(SO_2\), and \(O_2\) (the gases involved in the equilibrium) do not change.

Helium is inert and does not participate in the equilibrium reaction. Therefore, its addition does not affect the partial pressures of \(SO_3\), \(SO_2\), and \(O_2\).

Le Chatelier's Principle Application:

Le Chatelier's principle states that a system at equilibrium will respond to a disturbance by shifting its equilibrium position to counteract the disturbance. In this case, the disturbance is the increase in total pressure due to the addition of helium.

Effect on \(SO_3\) Dissociation:

The equilibrium involving \(SO_3\), \(SO_2\), and \(O_2\) will not shift because the partial pressures of these gases remain unchanged. Since the partial pressures do not change, there is no net change in the equilibrium position of the reaction. The concentration of \(SO_3\) (and the other gases) remains the same.

Conclusion: Based on the fact that the volume is constant and the partial pressures of \(SO_3\), \(SO_2\), and \(O_2\) do not change despite the increase in total pressure by adding helium: option (3) remains unaltered

This option correctly reflects the situation where the equilibrium position of the \(SO_3\) dissociation reaction remains unchanged. The addition of helium does not alter the partial pressures of the gases involved in the equilibrium reaction, hence there is no shift in equilibrium according to Le Chatelier's principle.